X; as an estimate of the population mean Problem 7. (10 POINTS) WEIGHTED SAMPLE MEAN In lectures, we discussed the sample mean X = =i. Let us consider a more general class of estimators: n X = wiXi, i=1 (4) where we are some weights. Note that the sample mean X, is a special case of (4) with w = 1/n. (a) (2 points) Under what condition on the weights, the estimate (4) is an unbiased estimate of ? (b) (8 points) Among all unbiased estimates of the form (4), find the most efficient estimate (i.e. the estimate with the smallest standard error).